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Functional equations for Weng's zeta functions for $(G,P)/\mathbb{Q}$
Functional equations Weng's zeta functions
2010/11/23
It is shown that Weng's zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equatio...
Improved Lower Bounds for Ginzburg-Landau Energies via Mass Displacement
Ginzburg-Landau Energies Mass Displacement
2010/11/24
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and th...
Approximation of functions and their derivatives by analytic maps on certain Banach spaces
Approximation of functions derivatives analytic maps
2010/11/24
Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous d...
Plurisubharmonic and holomorphic functions relative to the plurifine topology
Plurisubharmonic and holomorphic functions the plurifine topology
2010/11/23
A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly pl...
Symmetries of the transfer operator for $\Gamma_0(N)$ and a character deformation of the Selberg zeta function for $\Gamma_0(4)$
the transfer operator Selberg zeta function
2010/11/23
The transfer operator for $\Gamma_0(N)$ and trivial character $\chi_0$ possesses a finite group of symmetries generated by permutation matrices $P$ with $P^2=id$. Every such symmetry leads to a factor...
Natural extensions and entropy of $\alpha$-continued fractions
Natural extensions entropy
2010/11/23
We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domai...
Using the notion of complete compactness introduced by H. Saar, we define completely almost periodic functionals on completely contractive Banach algebras. We show that, if $(M,\Gamma)$ is a Hopf--vo...
The distribution functions of $\sigma(n)/n$ and $n/\phi(n)$, II
The distribution functions math
2010/11/23
Let $\sigma(n)$ be the sum of the positive divisors of $n$, and let $A(t)$ be the natural density of the set of positive integers $n$ satisfying $\sigma(n)/n \ge t$. We give an improved asymptotic re...
Green's functions for parabolic systems of second order in time-varying domains
Green's functions parabolic systems
2010/11/22
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz ...
On the Fekete-Szegö problem for concave univalent functions
the Fekete-Szegö problem concave univalent functions
2010/11/22
We consider the Fekete-Szeg\"o problem with real parameter $\lambda$ for the class $Co(\alpha)$ of concave univalent functions.
We derive a Mellin-Barnes integral representation for solution to generalized (parabolic) quantum Toda lattice introduced in \cite{GLO}, which presumably describes the $(S^1\times U_N)$-equivariant Gr...
New entropy conditions for scalar conservation laws with discontinuous flux
New entropy conditions scalar conservation laws discontinuous flux
2010/11/23
We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the ...
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...
A Note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices
Central Limit Theorem the Eigenvalue Counting Function
2010/11/23
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavi...
The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple
infinite dimensional convex set BV functions
2010/11/23
In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [1] by using Dirichlet form theory. By this definition, we can c...